Let's say that early 19th century South Carolina had 300000 freemen and 200000 slaves, would that mean that people back then would say that South Carolina had a population of 500000?
The U.S. census counted slaves. For example, in 1800, the census asked for:
under 10 years of age
of 10 years but under 16 years
of 16 years but under 26 years
of 26 years but under 45 years
45 years and upward
Number of all other free persons
Number of slaves
You can find all of the questions from all previous censuses on the Census Bureau's website, here.